A port-Dirac formulation for thermodynamics of non-simple systems

Hiroaki Yoshimura*, François Gay-Balmaz

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)


The paper presents a port-Dirac formulation for thermodynamics of non-simple systems, in which we consider a non-simple system whose thermodynamic states may be represented by several entropy variables. Here we regard such a non-simple system as an interconnected system with ports that can be represented by a port-Dirac system in the context of Dirac structures. We first show some extension of the Lagrange-d'Alembert principle for obtaining the evolution equations of such non-simple systems. Then, a Dirac structure is constructed on the Pontryagin bundle over a thermodynamic configuration manifold. Further, a port-Dirac dynamical formulation for such non-simple systems is demonstrated, where the developed evolution equations are to be equivalent with the generalized Lagrange-d'Alembert equations. The validity of the proposed approach is finally illustrated by two examples of an adiabatic piston and a resistive circuit with entropy production.

Original languageEnglish
Pages (from-to)32-37
Number of pages6
Issue number19
Publication statusPublished - 2021
Event7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021 - Berlin, Germany
Duration: 2021 Oct 112021 Oct 13


  • Adiabatic piston
  • Dirac structures
  • Electric circuit
  • Non-simple systems
  • Nonequilibrium thermodynamics

ASJC Scopus subject areas

  • Control and Systems Engineering


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